Gord was looking at these multiples of 9: 18, 45, 63, 72, 81, 108, 216. He claimed that the sum of the digits in any multiple of 9 will add to 9. Do you agree or disagree? Justify your decision.
What is your decision?
I know it might sound stupid, but I said that I disagreed with him. The sum of the digits in any multiple of 9 will not add to 9, because the number will get bigger and bigger as the number that it multiplied by 9 gets bigger. F.E., 9x4=36. The sum of the digits is 9, and the times they've been multiplied by 9 is 4 times. Was I completely wrong?
sorry, I meant the sum of the digits is 36 and not 9.
1+8=9
2+7=9
3+6=9
4+5=9
etc.
Keep going. What do you find?
"sum of the digits is 36" -- 3 + 6 = 9
2 + 1 + 6 = 9
28 * 9 = 252
2 + 5 + 2 = 9
Can you think of any sum of the digits in any multiple of 9 that will NOT add to 9?
Oh, multiple. I read it as multiply. I see why I'm wrong now, I kept thinking that the numbers have to be multiplied by 9, and not they have to be multiples of 9.
Thank you,
When I said "sum of the digits is 36", I had meant that 4x9=36 when I tried to offer an example. Though it makes sense that you reworded it, Thank you Ms. Sue and Writeacher once more.
You're welcome.
Gord was looking at these multiples of 9: 18, 45, 63, 72, 81, 108, 216. he claimed that the sum of the digits in any multiple of 9. do you agree or disagree? justify your decision.
I agree with Gord's claim that the sum of the digits in any multiple of 9 will add to 9. This is because 9 has a special property where it is the only non-zero digit where the sum of its factors (1 and itself) add up to 9. So any multiple of 9 will have factors that add up to 9, which means that the sum of the digits will add up to 9 as well. The provided examples of multiples of 9, such as 18 (1+8=9), 45 (4+5=9), and 81 (8+1=9), all follow this pattern.
Zoe made the following conjecture. (Zoe’s conjecture: when any number is multiplied by itself, the product will be greater than this starting number. For example, 3x3=9, the product is greater than the starting number 3.) Sage disagreed with Zoe’s conjecture. Sage pointed out that 1/3x1/3=1/9 and 1/9 is less than 1/3. How could Zoe’s conjecture be improved? Explain any change or changes you would make.
Zoe's conjecture could be improved by adding the qualifier "for positive numbers" to make it accurate. With this added qualifier, Zoe's conjecture would state that when any positive number is multiplied by itself, the product will be greater than the starting number.
This change is necessary because there are some instances where the product of a number multiplied by itself is less than the starting number. For example, if the number is between 0 and 1, such as 1/3, then the product of the number multiplied by itself will be smaller than the starting number. In this case, 1/9 is indeed less than 1/3. The qualifier "for positive numbers" would ensure that Zoe's conjecture only applies to positive numbers and not to all numbers in general.
Greens claimed that all natural numbers can be written as the sum of consecutive numbers. She based her conjecture on the following evidence.
7=3+4
15=1+2+3+4+5
33=10+11+12
120=22+23+24+25+26
Do you agree or disagree with Treena’s conjecture? Justify your reasoning.
I disagree with Treena's conjecture that all natural numbers can be written as the sum of consecutive numbers. Although the evidence she provides supports her conjecture, it does not prove it to be true for all natural numbers.
For example, some natural numbers such as 2, 4, 5, and 8 cannot be written as the sum of consecutive numbers. It's also worth noting that the examples Treena provides are not sufficient to prove her conjecture, as there could be other natural numbers that cannot be written as the sum of consecutive numbers that are not included in her examples.
In general, it is a well-known fact that most natural numbers can be written as the sum of consecutive numbers, and there are some formulas that can be used to calculate these sums. However, it is not true for all natural numbers, and therefore Treena's conjecture is not valid.
Determine the measure of angle Q to the nearest degree
I'm sorry, I cannot provide an answer without additional information or an accompanying diagram. Could you please provide more context or details for this question?
-2 x 52.4 x 50 x cos25 degrees
Using a calculator:
cos(25 degrees) = 0.9063 (rounded to four decimal places)
-2 x 52.4 x 50 x cos25 degrees = -91,881.1769
Rounding to the nearest whole number, the result is approximately: -91,881 degrees.
-2 x 52.4 x 50 x cos25 degrees to nearest tenth
Using a calculator:
cos(25 degrees) = 0.9063 (rounded to four decimal places)
-2 x 52.4 x 50 x cos25 degrees = -91,881.1769
Rounding to the nearest tenth, the result is approximately: -91881.2.
Square root of 405
The square root of 405 is approximately 20.1246117962 (rounded to 10 decimal places).
what are the question in acknowledge exam of drive learners license
I'm sorry, but I am not aware of the specific questions on the acknowledge exam for a driver's learner's license. The questions on this exam can vary depending on the country or state in which you are taking the exam. It would be best to consult the driver's license authority or the official handbook for your specific jurisdiction to get accurate and up-to-date information on the questions that may be included in the exam.
what are the question in acknowledge exam of Alberta drive learners license?
I apologize, but as an AI language model, I don't have access to real-time information or specific regional driving exams such as the Alberta driver's learner's license exam. The content and format of the exam may vary over time and can be subject to updates or changes by the respective authorities.
I would recommend visiting the official website of the Alberta Transportation or the Alberta Government to find the most accurate and up-to-date information regarding the knowledge exam for a learner's license. They should have resources available that outline the specific questions and topics covered in the exam, as well as any study guides or practice tests that may be useful in preparing for the exam.
Mario calculated square root of 2 using his calculator. Mario says square root of 2 that is equivalent to 1.4.
Mario's statement about the square root of 2 being equivalent to 1.4 is not entirely accurate. The exact value of the square root of 2 is an irrational number and is approximately equal to 1.41421356 (rounded to eight decimal places). While 1.4 is a close approximation, it is not an exact representation of the square root of 2.
Determine the area of the shape below length is 3 square root of 10 cm and width is 2 square root of 15 cm. Show your steps and express the answer in simplest mixed radical form.
To find the area of the shape, we multiply the length by the width.
Length = 3√10 cm
Width = 2√15 cm
Area = Length x Width
Area = (3√10 cm) x (2√15 cm)
To multiply the two square roots, we multiply the numbers outside the radical and the numbers inside the radical.
Thus, the area is:
Area = (3 x 2)√(10 x 15) cm²
Area = 6√(150) cm²
Now, let's simplify the radical. We look for any perfect square factors of 150.
150 = 25 x 6
Area = 6√(25 x 6) cm²
Taking the square root of 25, we have:
Area = 6 x 5√6 cm²
Finally, multiplying the remaining numbers outside the radical, we get:
Area = 30√6 cm²
So, the area of the shape is 30√6 cm² in simplest mixed radical form.
Solve each radical equation. *Recall that there are 3 basic steps to solving a radical equation (restriction, solve, verify).
To solve a radical equation, we follow these three basic steps: restriction, solve, and verify.
1. Restriction: Determine any restrictions on the variable that would cause the radicand (expression inside the radical) to be undefined. For example, if we have a square root, the radicand cannot be negative, so we restrict the variable to non-negative values.
2. Solve: Isolate the radical term and solve the equation for the variable.
3. Verify: Substitute the obtained solutions back into the original equation to ensure that they satisfy the equation.
Without a specific radical equation provided, I cannot solve a specific problem for you. Please provide a specific radical equation, and I will be happy to guide you through the steps of solving it.
Solve each radical equation. *Recall that there are 3 basic steps to solving a radical equation (restriction, solve, verify). (Sqrt20x-4 = 16)
Sure! Let's solve the radical equation:
Step 1: Restriction
For this equation, we have a square root (√) which requires the radicand (the expression inside the square root) to be non-negative. Therefore, we need to ensure that the expression inside the square root is greater than or equal to zero.
20x - 4 ≥ 0
Solving this inequality, we find:
20x ≥ 4
x ≥ 4/20
x ≥ 1/5
So, our restriction is x ≥ 1/5.
Step 2: Solve
Now, let's solve the equation:
√(20x - 4) = 16
First, we square both sides of the equation to get rid of the square root:
(√(20x - 4))^2 = (16)^2
20x - 4 = 256
Next, we isolate the variable:
20x = 256 + 4
20x = 260
x = 260/20
x = 13
So, the solution to the equation is x = 13.
Step 3: Verify
To verify if x = 13 is a valid solution, substitute it back into the original equation:
√(20(13) - 4) = 16
√(260 - 4) = 16
√256 = 16
16 = 16
Since 16 equals 16, the solution x = 13 satisfies the original equation.
Therefore, the solution to the radical equation √(20x - 4) = 16 is x = 13, with the restriction x ≥ 1/5.
Solve each radical equation. *Recall that there are 3 basic steps to solving a radical equation (restriction, solve, verify). Sqrt2a+1+6=3
Let's solve the radical equation step by step:
Step 1: Restriction
For this equation, we have a square root (√) which requires the radicand (the expression inside the square root) to be non-negative. Therefore, we need to ensure that the expression inside the square root is greater than or equal to zero.
2a + 1 + 6 ≥ 0
Simplifying the inequality, we have:
2a + 7 ≥ 0
Solving this inequality, we find:
2a ≥ -7
a ≥ -7/2
So, our restriction is a ≥ -7/2.
Step 2: Solve
Now, let's solve the equation:
√(2a + 1) + 6 = 3
First, let's isolate the radical term:
√(2a + 1) = 3 - 6
√(2a + 1) = -3
Since the square root cannot be a negative value, we know that there is no solution in this case. The equation has no real solutions because the radicand cannot be negative.
Step 3: Verify
Since we found no solution in Step 2, there is no need to perform the verification step.
Therefore, the given radical equation √(2a + 1) + 6 = 3 has no real solutions. The restriction is a ≥ -7/2.
*Remember that a dot like the one between the 5 and the cube root indicates multiplication. 5 • 3sqrt2t = 25
To solve the equation 5 • 3√(2t) = 25, we can follow these steps:
Step 1: Simplify the equation.
5 • 3√(2t) = 25
We can divide both sides of the equation by 5 to simplify it:
3√(2t) = 5
Step 2: Isolate the radical term.
To isolate the radical term, we need to get rid of the multiplication by 3. We can do this by dividing both sides of the equation by 3:
(3√(2t))/3 = 5/3
This simplifies to:
√(2t) = 5/3
Step 3: Square both sides of the equation.
To eliminate the square root, we square both sides of the equation:
(√(2t))^2 = (5/3)^2
2t = 25/9
Step 4: Solve for t.
Now, let's isolate t by dividing both sides of the equation by 2:
(2t)/2 = (25/9)/2
t = 25/18
So, the solution to the equation 5 • 3√(2t) = 25 is t = 25/18.
at the scene of an accident, a dry stretch of pavement has a drag factor of 0.75. the radius of a Yaw mark was determined to be 171 m. Determine the minimum speed, to the nearest km/h, the car was traveling at the time of applying brakes.
To determine the minimum speed of the car, we can use the formula for calculating minimum speed given the drag factor and radius of a yaw mark.
The formula for minimum speed is:
v = √(g * R * μ)
Where:
v is the minimum speed (in m/s)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
R is the radius of the yaw mark (in meters)
μ is the drag factor
Given:
R = 171 m
μ = 0.75
Plugging in the values into the formula:
v = √(9.8 * 171 * 0.75)
Calculating this, we find:
v ≈ 34.628 m/s (rounded to three decimal places)
To convert this speed into km/h, we can multiply by a conversion factor:
v ≈ 34.628 m/s * (3600 s/1 hr) * (1 km/1000 m)
Converting and rounding to the nearest km/h, the minimum speed is approximately:
v ≈ 124 km/h
Therefore, the minimum speed of the car at the time of applying brakes is approximately 124 km/h.
at the scene of an accident, a dry stretch of pavement has a drag factor of 0.75. the radius of a Yaw mark was determined to be 171 m. Determine the minimum speed, to the nearest km/h, the car was traveling at the time of applying brakes.
Where,
s = the speed (km/h) the vehicle was travelling when the brakes were applied
f = the drag factor of the surface
r = radius (m) of the curved Yaw mark
To determine the minimum speed (s) of the car at the time of applying brakes, we can use the following formula:
s = √(f * g * r)
Given:
f = 0.75 (drag factor)
r = 171 m (radius of the yaw mark)
g = 9.8 m/s² (acceleration due to gravity)
Substituting the given values into the formula:
s = √(0.75 * 9.8 * 171)
Calculating this, we find:
s ≈ 31.291 km/h (rounded to three decimal places)
Therefore, the minimum speed at which the car was traveling at the time of applying brakes is approximately 31 km/h.
s = sqrt127fr
Where,
s = the speed (km/h) the vehicle was travelling when the brakes were applied
f = the drag factor of the surface
r = radius (m) of the curved Yaw mark
at the scene of an accident, a dry stretch of pavement has a drag factor of 0.75. the radius of a Yaw mark was determined to be 171 m. Determine the minimum speed, to the nearest km/h, the car was traveling at the time of applying brakes.
To determine the minimum speed (s) of the car when the brakes were applied, we can use the given equation:
s = sqrt(127 * f * r)
Given:
f = 0.75 (drag factor)
r = 171 m (radius of the yaw mark)
Substituting the given values into the equation:
s = sqrt(127 * 0.75 * 171)
Calculating this, we find:
s ≈ 25
s = sqrt127fr
Where,
s = the speed (km/h) the vehicle was travelling when the brakes were applied
f = the drag factor of the surface
r = radius (m) of the curved Yaw mark
A car is traveling at a speed of 80km/h on an icy highway. The driver swerves while applying the brakes to avoid a collision. if the Yaw mark that the car leaves on the icy asphalt has a radius of 270 m, determine the drag factor of the icy highway. Round to the nearest hundredth.
A car is traveling at a speed of 80km/h on an icy highway. The driver swerves while applying the brakes to avoid a collision. if the Yaw mark that the car leaves on the icy asphalt has a radius of 270 m, determine the drag factor of the icy highway. Round to the nearest hundredth.
apply the distributive property (2 sqrt x - 1)(5 + sqrt x)
Written as an entire radical, Equation 5 cube root 4 is equivalent to
Written as an entire radical, Equation 5 cube root 4 is equivalent to?
state the vertex of f(x)=0.2(x-5)^2-8, then graph this function on the grid provided. Label any points you plot with the ordered pair.
determine the y-intercept of f(x)=0.2(x-5)^2 - 8, then graph this function on the grid provided. Label any points you plot with the ordered pair.
What is the value of x?
9 over 5 equals 2 over x
Select one:
a.
9 over 10
b.
10 over 9
c.
4 over 5
d.
5 over 4